In present paper, we propose efficient computational algorithms for simulation of the flow in deposits with intersecting fractures systems on unstructured PEBI (PErpendicular-BIsectional) grids adapted to geometrical features of well completions: direct flow calculation through the hydraulic fracturing crack on the PEBI grid, the Oda method to calculate effective medium parameters (full permeability tensor) on PEBI grids, EDFM (embedded discrete fracture model) on PEBI grids. Additionally, we propose an algorithm for modeling multilateral wells on the PEBI grid that factors in each wellbore trajectory. The proposed methods are developed for the isothermal three-phase flow problem, including phase transitions, gravity and capillary forces (the Black Oil model). The developed approach allows for correct simulation of both SRV fractures extensive network distribution features and adding new Fish-Bone wellbores, which enables physically based history matching and accurate and realistic forecast in reservoir modeling.